01 - Preheat oven to 400°F. Line a 10x15-inch rimmed baking sheet with parchment paper or lightly grease with butter.
02 - In a large bowl, combine flour, sugar, and salt. Cut in cold butter using a pastry blender or fingers until coarse crumbs form. Gradually add ice water, mixing just until dough comes together. Divide into two portions, one slightly larger than the other.
03 - On a floured surface, roll out the larger dough portion to fit the bottom and sides of the prepared pan. Carefully transfer dough to pan, pressing evenly into corners and up the sides.
04 - In a large bowl, combine sliced apples with both sugars, cinnamon, nutmeg, salt, cornstarch, and lemon juice. Toss thoroughly until apples are evenly coated.
05 - Spread apple mixture evenly over the bottom crust. Roll out remaining dough and place over apples. Trim excess dough, pinch edges to seal top and bottom crusts together, and cut several small slits in the top crust for steam ventilation.
06 - Whisk egg with milk until combined. Brush mixture evenly over the entire top crust. Sprinkle with coarse sugar if desired for extra crunch and shine.
07 - Bake for 35 to 40 minutes until crust is deep golden brown and filling bubbles visibly through the steam vents. If edges brown too quickly, cover with foil.
08 - Allow pie to cool for at least 30 minutes before slicing. This helps filling set and makes cleaner cuts. Cut into squares and serve warm or at room temperature.